Nano-Electron Fluidic Logic (NFL) Device

ABSTRACT

A nano-electron fluidic logic (NFL) device for controlling launching and propagation of at least one surface plasma wave (SPW) is disclosed. The NFL device comprises a metallic gate patterned with a plurality of terminals at which SPWs may be launched and a plurality of drain terminals at which the SPWs may be detected. A wave guiding structure such as a 2 DEG EF facilitates propagation of the SPW within the structure so as to scatter/steer the SPW in a direction different from a pre-scattering direction. A bias SPW is excited by an application of a control SPW with a momentum vector at an angle to the bias SPW and a control current with a wavevector which scatters the bias SPW in the direction of at least one output SPW, towards a drain terminal. The NFL device being rendered with device speed as a function of SPW propagation velocity.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of the provisional patentapplication No. 61/125,987 filed on Apr. 29, 2008

FEDERALLY SPONSORED RESEARCH

Not Applicable

SEQUENCE LISTING OR PROGRAM

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STATEMENT REGARDING COPYRIGHTED MATERIAL

Portions of the disclosure of this patent document contain material thatis subject to copyright protection. The copyright owner has no objectionto the facsimile reproduction by anyone of the patent document or thepatent disclosure as it appears in the Patent and Trademark Office fileor records, but otherwise reserves all copyright rights whatsoever.

BACKGROUND

The invention relates in general to digital logic circuits fabricated asintegrated circuits, and more particularly to a nano-electron fluidiclogic (NFL) device that operates by steering the propagation directionof a surface plasma wave (SPW) set up in an electron fluid (EF), withdevice speed as a function of SPW propagation velocity.

Advanced digital circuits for logic and digital applications fabricatedwith CMOS integrated technology become a dominant technology insemiconductor industry. The continuous improvement in the basic CMOSintegrated devices is attributed to scaling of the device's dimensionsfor enhancing speed. Without a commensurate increase in operating speed,the point of diminishing returns for CMOS scaling is imminent.Accordingly, new device concepts and technologies that may shift CMOSscaling necessitates another paradigm effectively utilizing manipulationof plasmons in a channel cavity.

Surface plasmons may exist on a boundary between two materials when thereal parts of dielectric constants have different signs, for example,between a metal and a dielectric. The material or structure forming theboundary with the material may be air, vacuum, or its equivalent, asubstantially homogeneous dielectric material, or a different materialor structure. The boundary, although being substantially continuous andplanar, may have different shapes. The plasmon, although includingsubstantially exponential functions with a field maximum at theboundary, may include only approximately exponential functions, may bedescribed by a different function, and/or may have a field maximum someplace other than the boundary.

Several optical waveguiding structures with the utilization of plasmonpropagation have been developed in the art. For example, U.S. Pat. No.6,977,767 issued to Sarychev discloses a method for controlling,guiding, manipulating, and circuiting light, and performingsurface-enhanced spectroscopy in medium comprising plasmonicnanomaterials via the excitation of plasmon modes in the materials. Theplasmonic nanomaterials are based on metal films with or without arraysof nanoholes and/or on metal nanowires and/or spheroids. There are alsodevices and methods employing such plasmonic nanomaterials. A deviceoperating according to the method may comprise integrated opticalelements to control light at telecommunications wavelengths betweenapproximately 1.3 microns to 1.6 microns. A device operating accordingto the method may comprise one or more photonic chips comprising one ormore photonic circuits.

U.S. Pat. No. 7,447,392 issued to Hyde discloses a plasmon gate and amethod of controlling energy propagation comprising guiding energy at afirst plasmon frequency along a first path, blocking the guided energyat the first plasmon frequency from propagating along the first pathresponsive to a first signal at a first time, blocking the guided energyat the first plasmon frequency from propagating along the first pathresponsive to a second signal, different from the first signal, at asecond time, and receiving an output that is a function of the firstsignal and the second signal.

There are many advanced digital circuits fabricated in CMOS technologywhich uses FET transistors for yielding high speed and low powerconsumption. For example, U.S. Pat. No. 5,001,367 issued to Vinalexplains a CMOS logic circuit that includes a driving stage having aplurality of parallel FETs of a first conductivity type for receivinglogic input signals and a load FET of second conductivity type connectedto a common output of the driving stage. A complementary FET inverterincluding serially connected FETs of the first and second conductivitytype is connected to the common output and the load FET. According tothe invention, the voltage transfer function of the complementaryinverter is skewed so that the product of the carrier mobility and theratio of channel width to length of the inverter FET of the firstconductivity type is made substantially greater than the product of thecarrier mobility and the ratio of channel width to the length of theinverter FET of the second conductivity type. By skewing the voltagetransfer function of the complementary inverter the voltage lift-offinterval is dramatically decreased, thereby improving the speed. Amultigate serial load transistor further reduces power consumption.

Hence it can be seen that the conventional MOS structures are limited invarious ways like increase in power consumption due to increased leakagecurrents, short channel effects, source-drain tunneling, pn junctiontunneling, decrease in channel mobility, increase in the interconnectionresistance concomitant with the smaller process geometries, and thelike. Advancements in submicron CMOS processing greatly benefit digitallogic and memory, but result in poor analog and RF performance and ahigh level of complexity in both lithography and design resulting inhigh manufacturing cost.

Although the above inventions serve a similar purpose, the object of thepresent invention is to provide a NFL device that operates by steeringthe propagation direction of a SPW set up in an electron fluid. Afurther object of the present invention is to provide a NFL device withdevice speed as a function of SPW propagation velocity. Other objects ofthe present invention will become better understood with reference tothe appended Summary, Description, and Claims.

SUMMARY

The present invention is a nano-electron fluidic logic (NFL) device forlaunching and controlling propagation of at least one surface plasmawave (SPW). The NFL device comprises a metallic gate patterned inaccordance with a plurality of geometrical parameters, such as aplurality of terminals at which a plurality of SPWs may be launched anda plurality of drain terminals at which the plurality of SPWs may bedetected. The plurality of geometrical parameters associated with themetallic gate includes width of at least one N-doped region, asource-drain channel length (L), and an angle (θ). The NFL device isfabricated as a metal-oxide-semiconductor (MOS) structure.

A wave guiding structure such as the 2 Dimensional Electron Gas,behaving as an Electron Fluid (2 DEG EF), a Luttinger liquid, or thelike, facilitates propagation of the SPW within the structure so as toscatter/steer the SPW in a direction different from a pre-scatteringdirection. The 2DEG EF steers the SPW with velocity about two orders ofmagnitude greater than that of electrons propagated thereby, resultingin plasmons. While inducing the 2DEG EF under the patterned metallicgate, a bias current may be launched into source bias terminal to excitethe SPW with at least one momentum vector. The bias SPW being excited byan application of at least one control SPW with a momentum vector at anangle to the at least one bias SPW and at least one control current withat least one wavevector which scatters the bias SPW in the direction ofat least one output SPW, substantially towards the at least one drainterminal.

Presence of at least one SPW at least one drain terminal is detected asa logic 1 and absence of the at least one SPW at the at least one drainterminal is detected as a logic 0. By controlling the launching of SPWs,according to a truth table, a flip-flop logic function may be realized.

Particularly, there are two modes of operation for the NFL devicethrough a sequence of events leading to the launching of the SPWs. Inthe first mode of operation, prior to launching the bias and controlSPWs, the 2DEG EF is created under the patterned gate by application ofthe proper gate voltage, resulting in a bias state, namely, a chargesheet equilibrium (neutral) standby state that can support thepropagation of SPWs, prior to the beginning of any logic operation. Thespeeds are dictated by the displacement of equilibrium electron density,relative to the positive background charge, and the SPW propagationvelocity. The speed of the SPW, calculated as displacement of the atleast one SPW in at least one direction is τ_(SPW) _(—)_(Displacement)=π/ω₀. The smallest switching time may be approximatelygiven by τ_(SPW) _(—) _(Displacement)+L/S_(SPW).

To ensure the adequate longevity of the SPW, its velocity must exceed acertain threshold velocity, ν_(Th), determined by both scattering andviscosity, and captured by an effective mean time between collisions, τ.If the propagation lengths of SPWs are sufficiently long, SPWs may beemployed for signal processing functions, the only energy required beingthat to launch them. The corresponding plasmon propagation velocity isgiven, where s_(2D)=√{square root over (e²n_(s)d/m*∈_(r)∈₀)}∈₀=8.854×10⁻¹² A²s⁴kg⁻¹m⁻³, ∈_(r)=12.9, the relative dielectric constantof a semiconductor, m*=0.067m₀, the electron effective mass,n_(s)=1×10¹⁶ m⁻², the free carrier density, and d=3 nm, the gate-channelseparation. Thus, the SPW may propagate a distance of 140 nm in 2.7 fs.In the presence of drain current, the SPW dispersion relation is givenby k=ω/(ν₀±s_(SPW)), where k is the wavevector, ν₀ is the electronvelocity, and s_(SPW) is the SPW velocity. The plus sign pertains topropagation along the direction of the current and the minus sign topropagation in an opposite direction of the current.

The plasmon velocity in the direction of current flow is increased, andin the opposite direction, it is reduced. Setting up a drain currentfacilitates achieving the condition for extending the propagation lengthof the SPW, and favoring the direction of current flow as the directionof propagation. A bias drain current with any nonzero value issufficient to extend the propagation length.

In the second mode of operation, the 2DEG EF is set up dynamically priorto launching the bias and control SPWs. The device speed may becontrolled by the parasitic effects and time constants associated withcharging the NFL gate capacitance. The preferred mode of NFL logic isself-timed for operation. In these modes of operations, the NFL circuitmay facilitate the SPWs to be launched by a light-plasmon coupling. Inaddition, the integration of devices results in the formation of the NFLarray, of which the arrangements may be utilized for parallel dataprocessing.

Two SPWs with momentum vectors {right arrow over (p)}_(Bias), {rightarrow over (p)}_(C2) and masses (energies) m_(Bias), M_(C2) respectivelyare excited/launched into terminals S_(Bias) and S_(C2), of thegeometrical parameters of the prototypical implementation, andpropagating on the 2DEG EF, upon interacting/colliding at thejunction/center of the structure, the SPW with momentum {right arrowover (p)}_(Bias) may be scattered (diverted/steered) by the SPW withmomentum {right arrow over (p)}_(C2) in the direction of output SPW{right arrow over (p)}_(O1). The probability that the SPW with momentumvector {right arrow over (k)}_(Bias) upon exposure to the SPW withmomentum vector {right arrow over (k)}_(C2) to divert by a solid angle(θ, φ) is given by dσ(θ, φ) as

${d\; \sigma_{2\leftarrow 2}} = \left. {\frac{1}{4\sqrt{\left( {p_{Bias} \cdot P_{C\; 2}} \right)^{2} - {m_{Bias}^{2}m_{C\; 2}^{2}}}}{\int_{\Delta}{\frac{d^{3}p_{{\overset{\rightarrow}{k}}_{O\; 1}}}{2{p_{{\overset{\rightarrow}{k}}_{O\; 1}}^{0}\left( {2\pi} \right)}^{3}}\frac{d^{3}p_{{\overset{\rightarrow}{k}}_{O\; 2}}}{2{p_{{\overset{\rightarrow}{k}}_{O\; 2}}^{0}\left( {2\pi} \right)}^{3}}}}}\  \middle| {{\langle{p_{{\overset{\rightarrow}{k}}_{O\; 1}},{p_{k_{O\; 2}}{}p_{Bias}},p_{C\; 2}}\rangle}^{2}\left( {2\pi} \right)^{4}{\delta^{(4)}\left( {p_{Bias} + p_{C\; 2} - p_{{\overset{\rightarrow}{k}}_{O\; 1}} - p_{{\overset{\rightarrow}{k}}_{O\; 2}}} \right)}} \right.$

where, p_(Bias) is the SPW with momentum vector {right arrow over(k)}_(Bias), p_(C2) is the control SPW with momentum vector {right arrowover (k)}_(C2), p_({right arrow over (k)}) _(O2) is the SPW in thedirection of {right arrow over (k)}₀₂, p_({right arrow over (k)}) _(O1)is the SPW in the direction of {right arrow over (k)}₀₁, ℑ is theplasmon-plasmon scattering amplitude, and Δ is the area/shell over whichintegration is performed.

Although particular embodiments of the present invention have beendescribed in the foregoing description, it is to be understood that thepresent invention is not to be limited to just the embodimentsdisclosed, but that they are capable of numerous rearrangements,modifications and substitutions without departing from the descriptionherein.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a top plan view of a NFL device for controlling activemanipulation of at least one SPW according to the present invention.

FIGS. 2A through 2D illustrate a qualitative manipulation andpropagation of at least one SPW on a 2 Dimensional Electron Gas (2DEG)and a subsequent realization truth table of a logic flip-flop.

FIG. 3 is an operational flow chart illustrating the launching andpropagation of at least one surface plasma wave (SPW) in a nano-electronfluidic logic (NFL) operation.

FIG. 4A is a nano-electron fluidic logic (NFL) circuit whereinpropagation of at least one surface plasma wave (SPW) is gated bygate-source voltages of at least one subsequent patterned gate.

FIG. 4B is a nano-electron fluidic logic (NFL) circuit whereinpropagation of at least one surface plasma wave (SPW) is enhanced bybias current.

FIG. 4C is a nano-electron fluidic logic (NFL) circuit wherein at leastone surface plasma wave (SPW) is launched by light-plasmon coupling.

FIG. 4D is a nano-electron fluidic logic (NFL) array whereinarrangements illustrated in FIGS. 4A through 4C may be utilized forparallel data processing.

FIG. 5 is a top plan view of a prototypical implementation of anano-electron fluidic logic (NFL) device of the present invention.

FIG. 5A is a cross sectional view taken along lines A-A′ of FIG. 5 ofthe present invention.

FIG. 5B is a cross sectional view taken along lines B-B′ of FIG. 5 ofthe present invention.

FIG. 5C is a cross sectional view taken along lines C-C′ of FIG. 5 ofthe present invention.

FIG. 5D is a cross sectional view taken along lines D-D′ of FIG. 5 ofthe present invention.

FIG. 6 is a dominant Feynman diagram for plasmon-plasmon scatteringaccording to the present invention.

FIG. 7A through 7C illustrate the diagrammatic representation of thescattering and interacting of the at least one surface plasma wave(SPW).

FIG. 8 is a graphical representation of plasmon-plasmon scatteringstrength as a function of normalized volume per conduction electron.

REFERENCE NUMERALS

-   -   10 . . . a nano-electron fluidic logic (NFL) device    -   12 . . . metallic gate    -   14, 16 . . . gate terminals    -   18 . . . source terminal    -   20, 22 . . . drain terminals    -   30 . . . pattern of momentum vectors    -   40 . . . flip-flop truth table    -   50 . . . operational flow chart for launching and propagating an        SPW    -   52 . . . creation of a 2DEG fluid    -   54 . . . launching of a bias SPW    -   56 . . . launching of control SPW    -   58 . . . scattering and propagation of a bias SPW    -   60 . . . detection of output SPW    -   70 . . . NFL circuit with SPW propagation gated by gate-source        voltage of subsequent gates    -   80 . . . NFL circuit with SPW propagation enhanced by bias        currents    -   90 . . . NFL circuit with SPWs launched by light-plasmon        coupling    -   100 . . . NFL array configuration for parallel data processing    -   110 . . . cross sectional view of semiconductor wafer taken        about the region of drain terminals    -   112 . . . semiconductor wafer    -   114 . . . n-type doping region    -   116 . . . metallic gate    -   118 . . . insulating layer    -   120 . . . cross sectional view of semiconductor wafer taken        about the region of source terminals    -   130,140 . . . cross sectional views of semiconductor wafer taken        about the regions of gate terminals    -   150 . . . dominant Feynman diagrams for plasmon-plasmon        scattering strength    -   160 . . . interaction between plasmons in a bubble contribution    -   170 . . . interaction between plasmons in a triangle        contribution    -   180 . . . interaction between plasmons in a square contribution    -   190 . . . graphical representation of plasmon-plasmon scattering        strength

DETAILED DESCRIPTION

Referring to the drawings, a preferred embodiment of a device forcontrolling launching and propagation of at least one surface plasmawave (SPW) in a nano-electron fluidic logic (NFL) operation isillustrated and generally indicated as 10 in FIGS. 1 through 8.

Referring to FIG. 1, a top plan view of a NFL device 10 for controllingactive manipulation of the at least one SPW is illustrated. The NFLdevice 10 comprises a metallic gate 12 patterned in accordance with aplurality of geometrical parameters, i.e., a plurality of terminals(S_(Bias), S_(C1), S_(C2)) 14, 16, 18 at which a plurality of SPWs maybe launched and a plurality of drain terminals (D_(O1), D_(C2)) 20, 22at which the plurality of SPWs may be detected. The manipulation of theat least one SPW at the source terminal 18 may be regulated by way of atleast one control SPW applied to at least one gate terminal 14,16. Theplurality of geometrical parameters associated with the metallic gate 12may include width of at least one N-doped region indicated as W0, W1,W2, W3, W4, W5, a source-drain channel length (L), and an angle (θ). Thewidths of the at least one N-doped region is at least equal to orgreater that of the patterned gate next to them, i.e., W1, W2, W3, W4,and W5 respectively. The NFL device 10 is fabricated as ametal-oxide-semiconductor (MOS) structure, where the patterned gate 12has thickness Tm, an oxide insulating layer of thickness Ti, and dopingof the semiconductor underneath of thickness Td.

Referring to FIGS. 2A through 2D, a qualitative SPW manipulation andpropagation on a 2 Dimensional Electron Gas (2DEG) that behaves as anElectron Fluid (EF) and a subsequent realization truth table 40 of alogic flip-flop (FF) (not shown). Typically, a waveguiding structuresuch as the 2DEG EF, a Luftinger liquid or the like facilitatespropagation of the SPW so as to scatter/steer the SPW in a directiondifferent from a pre-scattering direction. The 2DEG EF steers the SPWwith velocity about two orders of magnitude greater than that ofelectrons propagated thereby resulting in plasmons. While inducing the2DEG EF under the patterned metallic gate 12, a bias current may belaunched into source bias terminal (S_(Bias)) 18 to excite the SPW withat least one momentum vector ({right arrow over (k)}_(Bias), {rightarrow over (k)}₀₁, {right arrow over (k)}₀₂). The bias SPW being excitedby an application of at least one momentum vector ({right arrow over(k)}_(Bias)) and at least one control current (I_(C1), I_(C2)) with atleast one wavevector ({right arrow over (k)}_(Bias), {right arrow over(k)}_(C1), {right arrow over (k)}_(C2)) scatters the bias SPW in thedirection of at least one output SPW, substantially towards the at leastone drain terminal (D_(O1), D_(O2)) 20, 22.

With reference to FIG. 2A, the NFL device 10 illustrates the 2DEG EF anda bias current I_(Bias) and a control current I_(C2) passingtherethrough. In the absence of the control SPWs which could otherwisebe launched from either the source C1 or source C2 terminals, the biasSPW would be split substantially into equal portions that may bedetected at least one drain terminal (D_(O1), D_(O2)) 20, 22. FIG. 2Billustrates SPWs with momentum vectors {right arrow over (k)}_(Bias) and{right arrow over (k)}_(C2) excited and launched into terminals S_(Bias)and S_(C2) and propagate on 2DEG EF. Upon reaching the junction, in thecenter of the structure 10 the SPW with {right arrow over (k)}_(Bias) isscattered/steered by the SPW with momentum {right arrow over (k)}_(C2)in the direction of output SPW {right arrow over (k)}₀₁ that exitsthrough the drain D_(O1) terminal 20. FIG. 2C illustrates a control SPWwith a wavevector {right arrow over (k)}_(Bias) diverts the bias SPW indirection of output {right arrow over (k)}₀₁. The presence of SPW {rightarrow over (k)}₀₁ at D_(O1) 20 is detected as a logic 1. The absence ofa SPW {right arrow over (k)}₀₁ at D_(O1) 20 is detected as a logic 0. Asshown in FIG. 2C, conservation of SPW momentum determines {right arrowover (k)}₀₁. By controlling the launching of SPWs, according to thetruth table 40 shown in FIG. 2D, the flip-flop logic function may berealized.

FIG. 3 is an operational flow chart 50 illustrating the launching andpropagation of at least one surface plasma wave (SPW) in a nano-electronfluidic (NFL) operation. A patterned two-dimensional electron gas (2DEG)that behaves as an electron fluid is created underneath at least onepatterned metallic gate as indicated at block 52. At block 54, the atleast one bias SPW is launched on the 2DEG fluid. At block 56, at leastone control SPW at an angle to the at least one bias SPW is launched onthe 2DEG. The at least one bias SPW is scattered to propagate on the2DEG fluid as indicated at block 58. At block 60, at least one outputSPW is detected in the direction of at least one drain terminal (D_(O1),D_(O2)) 20, 22.

Referring to FIGS. 4A through 4D, an examination of the principles ofoperation of NFL, in light of circuits and systems considerations isillustrated which elicit the ultimate device density, the ultimatedevice speed, integration of many devices resulting in formation of anNFL array that eliminates cross talk, forming interconnections betweengates, interfacing NFL to conventional electronics and clocking of thesedevices via opto-electronic techniques.

FIG. 4A is a NFL circuit 70 wherein propagation of at least one SPW isgated by gate-source voltages of at least one subsequent patterned gate12. FIG. 4B illustrates a NFL circuit 80 wherein propagation of at leastone SPW is enhanced by bias current. FIG. 4C illustrates a NFL circuit90 wherein at least one SPW is launched by light-plasmon coupling. FIG.4D is a NFL array 100 wherein arrangements illustrated in FIGS. 4Athrough 4C may be utilized for parallel data processing.

Typically, SPW reflection within the channel (source-drain) cavity needsto be avoided in predetermined operating conditions. Therefore, thedevice density limits by that at which a resonance may occur. As theresonance frequency is ω₀=πs_(SPW)/2L, a trade-off exists betweenoperating frequency and channel length and device density. The ultimatedevice density is that of the smallest possible plasmon. Therefore, theultimate density, which suggests a greater equivalent density, may beequal to the areal atomic density of the material utilized.

Particularly there are two modes of operation for the NFL device 10through a sequence of events leading to launching the SPWs. In the firstmode of operation, prior to launching the bias and control SPWs, the2DEG EF is created under the patterned gate 12 by the application of theproper gate voltage such as V_(G1), V_(G2), . . . V_(GN). This resultsin a bias state, namely, a charge sheet equilibrium (neutral) standbystate that can support the propagation of SPWs, prior to the beginningof any logic operation. This state may be set at, e.g., the power up ofthe system, and the speed of any subsequent logic operation can bedetermined by the speeds at which the SPWs may be generated andpropagated. These speeds are dictated by the displacement of equilibriumelectron density, relative to the positive background charge, and theSPW propagation velocity.

The speed of the SPW calculated as displacement of the at least one SPWin at least one direction is given by τ_(SPW) _(—) _(Displacement)=π/ω₀,where ω₀ is the plasma oscillation frequency. The smallest switchingtime may be approximately given by τ_(SPW) _(—)_(Displacement)+L/S_(SPW), where L is the source-drain distance; ands_(SPW) is the SPW velocity. The presence of a bias source-drainpotential difference, which can be set up prior to any logic operation,if desired, establishes a baseline drift velocity ν₀ that may extend thelife/propagation distance of the “bias” and “control” SPWs.

In the absence of drain current, application of a large gate-sourcebias, U₀ disturbs the high-density charge sheet equilibrium and resultsin the creation of an SPW with linear dispersion, which propagates witha wave velocity S_(L)=√{square root over (eU₀/m*)}. Thus, thehigh-density carrier sheet acts as an SPW waveguide structure. Themaximum length of propagation, however, is limited by two main decaymechanisms, namely, electron scattering by phonons or impurities,captured by the momentum relaxation time, τ_(p), and the viscosity ofthe electron fluid, ν=ν_(F)λ_(ee) where, ν_(F) is the Fermi velocity andλ_(ee) is the average distance between electrons. The viscosity givesrise to a damping time constant τ_(ν)=νk². The ability of an SPW ofvelocity ν_(SPW) to propagate a distance L, then, depends on whether theconditions L/ν_(SPW)<½τ_(p) and L/ν_(SPW)<τ_(ν) are satisfied. To ensurethe adequate longevity of the SPW, its velocity must exceed a certainthreshold velocity, ν_(Th), determined by both scattering and viscosity,and captured by an effective mean time between collisions, τ. If thepropagation lengths of SPWs are sufficiently long, SPWs may be employedfor signal processing functions, the only energy required being that tolaunch them.

The plasma oscillations may be visualized as resulting from the motionof electron density in the 2 DEG, of total mass m, with respect to thepositive background charge and its motion under the electrostaticrestoring force that allows to estimate the maximum stored energy as,E_(s)=mν_(sat) ²/2, where ν_(sat) is the saturation velocity ofelectrons. The energy spent in setting the plasmon into motion is givenby E_(d)=E_(s)/Q, where Q is the quality factor of the system. As withany other oscillating system, the Q of the 2DEG is given byQ=ω₀/2α=ω₀R_(2DEG)/2L_(2DEG), where ω₀ is the plasma frequency, α is thedamping constant and R_(2DEG)=m*/ne²Aτ and L_(2DEG)=m*/ne²A are the 2DEGresistance and kinetic inductance respectively. Thus, the energydissipated to launch the at least one plasmon in the 2DEG fluid is givenby E_(d)=mν_(sat) ²/2ω₀τ where ω₀ is the plasma oscillation frequency,and τ, the effective mean time between collisions.

For a gated 2DEG with the gate-source bias, U₀, k≅√{square root over(2πn_(s))}. The corresponding plasmon propagation velocity is given byS_(2D)=√{square root over (e²n_(s)d/m*∈_(r)∈₀)} where ∈₀=8.854×10⁻¹²A²s⁴kg⁻¹m⁻³, ∈_(r)=12.9, the relative dielectric constant of asemiconductor, m*=0.067m₀, the electron effective mass, n_(s)=1×10¹⁶m⁻², the free carrier density, and d=3 nm, the gate-channel separation.Thus, the SPW may propagate a distance of 140 nm in 2.7 fs. Signalprocessing functions based on SPWs of long propagation lengths may be anextremely low-power dissipation and high-speed technology. For anungated 2DEG, with grounded source and open drain, k=π(2l−1)/2L, where Lis the source-drain distance and l is an integer standing for the modeindex.

In the presence of drain current, the SPW dispersion relation is givenby k=ω/(ν₀±s_(SPW)), where k is the wavevector, ν₀ is the electronvelocity, and s_(SPW) is the SPW velocity. The plus sign pertains topropagation along the direction of the current and the minus sign topropagation in an opposite direction of the current.

The plasmon velocity in the direction of current flow is increased, andthat in the opposite direction is reduced, setting up a drain currentwhich facilitates achieving the condition for extending the propagationlength of the SPW, and favoring the direction of current flow as thedirection of propagation. Thus, a bias drain current may be necessary incertain SPW propagation applications. If the material quality is suchthat in the absence of drain current the plasmons can propagate tens ofnm, the impact of bias current on power dissipation is negligible, sincein principle any nonzero value of current may be sufficient to extendthe propagation length.

In the second mode of operation, the 2DEG EF is set up dynamically priorto launching the bias and control SPWs. The device speed, then, may becontrolled by the parasitic effects and time constants associated withcharging the NFL gate capacitance. This mode of operation, and thepotential speed penalty incurred, however, is justified only whenever itbecomes necessary to interface with CMOS logic. The preferred mode ofNFL logic is self-timed for operation. In these modes of operations, theNFL circuit may facilitate the SPWs to be launched by a light-plasmoncoupling. In addition, the integration of devices results in formationof the NFL array 100, wherein arrangements may be utilized for paralleldata processing.

FIG. 5 is a top plan view of a prototypical implementation of the NFLdevice 10 of the present invention. FIG. 5A through 5D are crosssectional views 110, 120, 130, 140 of FIG. 5 taken along lines A-A′,B-B′, C-C′ and D-D′ respectively. The cross sectional configurationincludes a semiconductor wafer 112 underneath the structure 10 which ispatterned with the N-Type doping (Td, W5) 114, a metal gate (Tm, W5) 116and an insulating layer (Ti, W5) 118 arranged between the N-doped region114 and the metal gate 116. The prototypical NFL device 10 with thegeometry of FIG. 5, may have the following parameters: 1)1.2 nm gateoxide; 2) 1200 Å n⁺ poly gate; 3) n-type (MOSFET-like) sources anddrains; 4) W1=W2=70.7 nm; 5) W3=W4=30 nm; 5) W0=100 nm; 6) L0=200 nm; 7)L1=30 nm; 7) L2=50 nm; 8) θ/2˜30°; 9)β˜45° This prototypical NFL device10 may exhibit a threshold gate voltage to induce the 2DEG EF U₀˜0.35 V.

Referring to FIG. 6, dominant Feynman diagrams 150 for plasmon-plasmonscattering are illustrated. Two SPWs with momentum vectors {right arrowover (p)}_(Bias), {right arrow over (p)}_(C2) and masses m_(Bias),m_(C2) respectively are excited/launched into terminals S_(Bias) andS_(C2), of the geometrical parameters of the prototypical implementation10, and propagating on the 2DEG EF, upon interacting/colliding at thejunction/center of the structure 10, the SPW with momentum {right arrowover (p)}_(Bias) may be scattered (diverted/steered) by the SPW withmomentum {right arrow over (p)}_(C2) in the direction of output SPW{right arrow over (p)}_(O1). The probability that the SPW with momentumvector {right arrow over (k)}_(Bias) upon exposure to the SPW withmomentum vector {right arrow over (k)}_(C2) to divert by a solid angle(θ, φ) is given by dσ(θ,φ) as

${d\; \sigma_{2\leftarrow 2}} = \left. {\frac{1}{4\sqrt{\left( {p_{Bias} \cdot P_{C\; 2}} \right)^{2} - {m_{Bias}^{2}m_{C\; 2}^{2}}}}{\int_{\Delta}{\frac{d^{3}p_{{\overset{\rightarrow}{k}}_{O\; 1}}}{2{p_{{\overset{\rightarrow}{k}}_{O\; 1}}^{0}\left( {2\pi} \right)}^{3}}\frac{d^{3}p_{{\overset{\rightarrow}{k}}_{O\; 2}}}{2{p_{{\overset{\rightarrow}{k}}_{O\; 2}}^{0}\left( {2\pi} \right)}^{3}}}}}\  \middle| {{\langle{p_{{\overset{\rightarrow}{k}}_{O\; 1}},{p_{{\overset{\rightarrow}{k}}_{O\; 2}}{}p_{Bias}},p_{C\; 2}}\rangle}^{2}\left( {2\pi} \right)^{4}{\delta^{(4)}\left( {p_{Bias} + p_{C\; 2} - p_{{\overset{\rightarrow}{k}}_{O\; 1}} - p_{{\overset{\rightarrow}{k}}_{O\; 2}}} \right)}} \right.$

where, p_(Bias) is the SPW with momentum vector {right arrow over(k)}_(Bias), p_(C2) is the control SPW with momentum vector {right arrowover (k)}_(C2), p_({right arrow over (k)}) _(O2) is the SPW in thedirection of {right arrow over (k)}₀₂, p_({right arrow over (k)}) _(O1)is the SPW in the direction of {right arrow over (k)}₀₁, ℑ is theplasmon-plasmon scattering amplitude, and Δ is the area/shell over whichintegration is performed.

Referring to FIGS. 7A through 7C, a diagrammatic representation of thescattering and interacting of the at least one SPW is illustrated. Thesolid lines denote electrons (→) and holes (←), respectively. The dotsdenote the Bohm-Pines vertices for electron-plasmon interactions. Theinteractions between plasmons captured by kernel, K(k₁k₂; k₃k₄), may berepresented as bubble contributions 150, triangle contributions 160, andsquare contributions 170. Accordingly, the interaction between plasmonscaptured by the kernel may be expressed as K=K_(B)+K_(T)+K_(S) whereK_(B) stands for terms arising from two γ₄'s (B for bubbles), K_(T)stands for terms arising from one γ₄ and two γ₃'s (T for triangles), andK_(S) stands for terms arising from four γ₃'s (S for square). Out ofthese contributions to the kernel, the triangle and square parts arenegligible with respect to the bubble contributions. The essence of thebubble contribution is given by the strength of the plasmon-plasmoncoupling, g₄(Q)≅4ω₀ ²K_(s)(Q+k, −k; Q+k′, −k′) where Q is the totalmomentum.

FIG. 8 is a graphical representation of plasmon-plasmon scatteringstrength as a function of normalized volume per conduction electron.Using the dispersion relation,

${g_{4}\left( {{Q = 0},{\omega = {2\omega_{0}}}} \right)} = {\frac{\mu \mspace{11mu} k_{F}}{F_{0}^{2}}\frac{5\alpha \; r_{s}}{192\pi^{5}} \times {\int_{\underset{{p^{\prime} - k^{\prime}} < \beta}{k^{\prime} < \beta}}\mspace{7mu} {{p^{\prime}}{k^{\prime}}\frac{\left\lbrack {\left( {p^{\prime} - k^{\prime}} \right) \cdot k^{\prime}} \right)^{2}}{{{p^{\prime} - k^{\prime}}}^{4}k^{\prime 2}} \times \begin{pmatrix}{\frac{1}{k^{\prime 2}} +} \\\frac{1}{k^{\prime 2} + {5{\omega_{0}^{2}/3}}}\end{pmatrix}{S_{SH}\left( p^{\prime} \right)}}}}$

where,F₀(Q=0, ω=2ω₀)=(μk_(F)/π²)×[−β+√{square root over (5ω₀ ²/12)}tan⁻¹(β/√{square root over (5ω₀ ²/3)})] and β=k_(e)/k_(F). S_(HF)(p′)denotes the Hartree-Fock structure factor and r_(s)=(¾πn_(s))^(1/3)/α₀.α₀=h²/me² and α≅ 1/137 is the fine structure constant. Using thisequation, g4 may be calculated for various values of, r_(s) from 1 to 10as shown in FIG. 7. The sign of g4 is positive for all r_(s), therebythe plasmon-plasmon interaction is repulsive. The SPWs interacting inthe junction of the device may be steered/scattered as prescribed bymomentum conservation principles.

All features disclosed in this specification, including any accompanyingclaims, abstract, and drawings, may be replaced by alternative featuresserving the same, equivalent or similar purpose, unless expressly statedotherwise. Thus, unless expressly stated otherwise, each featuredisclosed is one example only of a generic series of equivalent orsimilar features.

Although preferred embodiments of the present invention have been shownand described, various modifications and substitutions may be madethereto without departing from the spirit and scope of the invention.Accordingly, it is to be understood that the present invention has beendescribed by way of illustration and not limitation.

1. A nano-electron fluidic logic (NFL) device that controls propagationof at least one surface plasma wave (SPW) in a waveguiding structure,the device comprising: a metallic gate patterned in accordance with aplurality of geometrical parameters; a plurality of source terminalssuch as S_(Bias), S_(C1), S_(C2), at which the plurality of SPWs may belaunched; and a plurality of drain terminals such as D_(O1), D_(O2) atwhich the plurality of SPWs may be detected; whereby the NFL deviceoperates by controlling the propagation direction of at least one SPWresulting speed in femto-seconds at femto-joules power dissipation. 2.The device of claim 1, wherein a bias current may be utilized to excitethe at least one SPW with at least one momentum vector ({right arrowover (k)}_(Bias), {right arrow over (k)}₀₁, {right arrow over (k)}₀₂).3. The device of claim 1, wherein the waveguiding structure may be apatterned two-dimensional electron gas (2DEG), the 2DEG being biased soas to behave as an electron fluid (EF).
 4. The device of claim 3,wherein the 2DEG steers the at least one SPW with velocity about twoorders of magnitude greater than that of electrons propagate.
 5. Thedevice of claim 3, wherein the waveguiding structure causes anexcitation to the at least one SPW resulting in at least one plasmon. 6.The device of claim 1, wherein the waveguiding structure may be aLuttinger liquid.
 7. The device of claim 6, wherein the waveguidingstructure causes an excitation to the at least one SPW resulting in atleast one plasmon.
 8. The device of claim 7, wherein the energydissipated to launch the at least one plasmon in the 2DEG of total massm is given by E_(d)=mν_(sat) ²/2ω₀τ, wherein ν_(sat) is the saturationvelocity of electrons; ω₀ is the plasma oscillation frequency; and τ isthe effective mean time between collisions.
 9. The device of claim 8,wherein the propagation velocity is given byS _(2D)=√{square root over (e ² n _(s) d/m*∈ _(r)∈₀)} wherein∈₀=8.854×10⁻¹² A²s⁴kg⁻¹m⁻³; ∈_(r)=12.9, the relative dielectric constantof a semiconductor; m*=0.067m₀, the electron effective mass;n_(s)=1×10¹⁶ m⁻², the free carrier density; d=3 nm, the gate-channelseparation;
 10. The device of claim 1, wherein the at least one SPWbeing excited by an application of at least one momentum vector ({rightarrow over (k)}_(Bias)) and at least one control current (I_(C1),I_(C2)) with at least one wavevector ({right arrow over (k)}_(Bias),{right arrow over (k)}_(C1), {right arrow over (k)}_(C2)) scatters theat least one SPW in the direction of at least one output SPW.
 11. Thedevice of claim 10, wherein a probability that the at least one SPW withmomentum vector {right arrow over (k)}_(Bias) upon exposure to the atleast one SPW with momentum vector {right arrow over (k)}_(C2) to divertby q solid angle (θ, φ) is given by dσ(θ,φ) as${d\; \sigma_{2\leftarrow 2}} = \left. {\frac{1}{4\sqrt{\left( {p_{Bias} \cdot P_{C\; 2}} \right)^{2} - {m_{Bias}^{2}m_{C\; 2}^{2}}}}{\int_{\Delta}{\frac{d^{3}p_{{\overset{\rightarrow}{k}}_{O\; 1}}}{2{p_{{\overset{\rightarrow}{k}}_{O\; 1}}^{0}\left( {2\pi} \right)}^{3}}\frac{d^{3}p_{{\overset{\rightarrow}{k}}_{O\; 2}}}{2{p_{{\overset{\rightarrow}{k}}_{O\; 2}}^{0}\left( {2\pi} \right)}^{3}}}}}\  \middle| {{\langle{p_{{\overset{\rightarrow}{k}}_{O\; 1}},{p_{{\overset{\rightarrow}{k}}_{O\; 2}}{}p_{Bias}},p_{C\; 2}}\rangle}^{2}\left( {2\pi} \right)^{4}{\delta^{(4)}\left( {p_{Bias} + p_{C\; 2} - p_{{\overset{\rightarrow}{k}}_{O\; 1}} - p_{{\overset{\rightarrow}{k}}_{O\; 2}}} \right)}} \right.$wherein, p_(Bias) is the SPW with momentum vector {right arrow over(k)}_(Bias); p_(C2) is the control SPW with momentum vector {right arrowover (k)}_(C2); p_({right arrow over (k)}) _(O2) is the SPW in thedirection of {right arrow over (k)}₀₂; p_({right arrow over (k)}) _(O1)is the SPW in the direction of {right arrow over (k)}₀₁; ℑ is theplasmon-plasmon scattering amplitude; and Δ is the area/shell over whichthe integration is performed.
 12. The device of claim 10, wherein the atleast one SPW substantially diverts in a direction of at least onemomentum drain vector ({right arrow over (k)}₀₁,{right arrow over(k)}₀₂) causing an increase in at least one drain current (I_(O1),I_(O2)).
 13. The device of claim 10, wherein presence of the at leastone output SPW ({right arrow over (k)}₀₁, {right arrow over (k)}₀₂) atleast one drain terminal (D_(O1), D_(O2)) is detected as a logic
 1. 14.The device of claim 10, wherein absence of the at least one output SPW({right arrow over (k)}₀₁, {right arrow over (k)}₀₂) at least one drainterminal (D_(O1), D_(O2)) is detected as a logic
 0. 15. The device ofclaim 1, wherein speed of the device is a function of SPW propagationvelocity in terahertz switching frequencies.
 16. The device of claim 1,wherein dispersion relation of the at least one SPW in the presence ofdrain current is given by k=ω/(ν₀±s_(SPW)), wherein k is the wavefactor;ν₀ is the electron velocity; and s_(SPW) is the SPW velocity.
 17. Thedevice of claim 16, wherein the plus sign pertains to propagation alongthe direction of the current.
 18. The device of claim 16, wherein theminus sign pertains to propagation in the opposite direction of thecurrent.
 19. The device of claim 1, wherein speed of the at least oneSPW calculated as displacement of the at least one SPW in at least onedirection is given byτ_(SPW) _(—) _(Displacement)=π/ω₀ wherein ω₀ is the plasma oscillationfrequency.
 20. The device of claim 1, wherein the smallest switchingtime may be approximately given byτ_(SPW) _(—) _(Displacement) +L/S _(SPW) wherein L is the source-draindistance; and s_(SPW) is the SPW velocity.
 21. A nano-electron fluidiclogic (NFL) device that controls propagation of at least one biassurface plasma wave (bias SPW) in the absence of at least one controlSPW in a wave guiding structure, the device comprising: a metallic gatepatterned in accordance with a plurality of geometrical parameters; aplurality of source terminals such as S_(Bias), S_(C1), S_(C2), at whichthe plurality of SPWs may be launched; and a plurality of drainterminals such as D_(O1), D_(O2), at which the plurality of SPWs may bedetected; whereby the bias SPW splits substantially into equal portionsthat may be detected at least one drain terminals (D_(O1), D_(O2)). 22.A method for controlling the launching and propagation of at least onesurface plasma wave (SPW) in a nano-electron fluidic logic (NFL)operation, the method comprising the steps of: creating a patternedtwo-dimensional electron gas (2DEG) underneath at least one patternedmetallic gate, the 2DEG being biased so as to behave as an electronfluid (EF); launching the at least one bias SPW on the 2DEG fluid;launching at least one control SPW at an angle to the at least one biasSPW on the 2DEG fluid; scattering the at least one bias SPW to propagateon the 2DEG fluid; and detecting at least one output SPW in thedirection of at least one drain terminal (D_(O1), D_(O2)).
 23. Themethod of claim 22, wherein presence of the at least one output SPW atthe at least one drain terminal (D_(O1), D_(O2)) is detected as alogic
 1. 24. The method of claim 22, wherein absence of the at least oneoutput SPW at the at least one drain terminal (D_(O1), D_(O2)) isdetected as a logic 0.